A Comparison of Logistic Regression Goodness-of-Fit Statistics When Applied to the Log Link

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Steve John Quinn*+ and Leigh Blizzard and David W. Hosmer
• Companies: Menzies Research Institute and Menzies Research Institute and University of Massachusetts, Amherst
• Keywords: log binomial ; goodness-of-fit

Abstract

Blizzard L & Hosmer DW (2006) contributed to the development of the log binomial regression model for binary outcomes that make it possible to directly estimate relative risk in follow-up studies, and prevalence ratios in cross-sectional studies, and to adjust for continuous covariates. There are several goodness-of-fit statistics that describe how well a logistic regression model fits a set of observations, but to date little work has been done that summarizes the discrepancy between observed and expected values for log link models. Through extensive simulations we compare the performance of several goodness-of-fit statistics via rejection rates, power to detect an incorrectly model, and power to detect an incorrectly specified link when applied to log link models.